B757 FLC WAS DISTRACTED AFTER TKOF BY AUTOTHROTTLE PROB AND WHEN ENGAGING LNAV THE ACFT TURNED; NOT IN ACCORDANCE WITH THE DEP PROC. DEP CTLR QUESTIONED THEIR TURN.

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ON TKOF ROLL CAPT COULD NOT GET AUTOTHROTTLES ENGAGED (RWY 24L LAX). DECISION TO GO AND SOLVE PROB IN THE AIR. ONCE AIRBORNE AND GEAR UP FLAP RETRACTION ON SCHEDULE; CAPT TRIED MANY DIFFERENT THINGS TO SOLVE PROB; IE: RECYCLING FMC; DIRECT VNAV/LNAV; AND FLT DIRECTORS. I WAS FLYING THE AIRPLANE. THE CAPT AND I THOUGHT IT WAS A TMC PROB (THRUST MODE CTL). I COMMUNICATED TO HIM I HAD A LIST OF CIRCUIT BREAKERS FOR THAT HIGHLIGHTED IN MY BOOK. I THEN NOTICED THAT DURING HIS TRYING DIFFERENT THINGS HE LEFT THE FLT DIRECTORS OFF. I ASKED HIM TO TURN THE FLT DIRECTORS ON AND ENGAGE VNAV/LNAV. AS I WATCHED HIM DO THIS; I NOTICED THE AUTOTHROTTLES SWITCH WAS OFF. AS THE LNAV ENGAGED AND COMMENCED A L TURN I FOLLOWED THE FLT DIRECTOR AND POINTED OUT THE SWITCH TO THE CAPT. HE TURNED ON THE SWITCH AND SOLVED OUR PROB. AT WHICH TIME ATC CALLED AND ASKED WHY WE WERE TURNING OFF. THE SID (LAXX2) RWY 24L CALLS FOR A 250 DEG HDG FOR VECTORS. BY ENGAGING LNAV THE FLT DIRECTORS COMMANDED US TO FLY THE SID. FORTUNATELY THERE WERE NO OTHER ACFT IN THE AREA. THE CAPT MISSED PART OF HIS PREFLT FLOW; THERE WAS NO CHKLIST ITEM TO BACK IT UP. I ALLOWED MYSELF TO BE DISTR FROM MY DUTY OF FLYING THE AIRPLANE AND GET INVOLVED IN THE PROB SOLVING. ANOTHER KEY LESSON HERE IS TO NOT LET THE TECHNOLOGY RUN YOU AS A PLT. THE PLT HAS TO RUN/MANAGE THE TECHNOLOGY.